Is this a bug in the mirror modifier?
I believe this is intentional. Other actions can trigger this behavior as well, such as switching to object mode and back instead of using undo.

I'm no developer, but I think I may know why this is the way it is.

First, the point of wireframe view is (usually) to be able to see through your mesh. It can also be quite handy to observe the structure of your mesh as well. However, the wireframe view can get very complex very quickly, especially when dealing with complex models. To help simplify this, Blender hides certain edges from display that it determines aren't adding much to the overall wireframe view. In object mode, this occurs as well. It's not too extreme usually, and there is an option to force Blender to draw all edges in Object mode, which can be found in the display panel of the Object tab in the properties panel.

It appears that this process of hiding certain edges is executed for certain operations only. Some of these include using undo, or switching modes. When adding new geometry, such as wit the loop tool or subdivide, it displays all the new edges.

The reason that the edge is determined to be 'not necessary to show' is that it doesn't really add anything to the wireframe view, since it could technically be removed and the resulting mesh object would be the same when viewed with solid shading. Another way to understand when an edge will be drawn or not is to view your object in solid view. If you cannot see your edge, such as in your case, it won't be drawn in wireframe view. If you make the edge meaningful in terms of it's contribution to the structure of you mesh, such as by moving the edge up along the Z axis, the next time you update the mesh, such as by switching modes, it will be displayed.

So to directly answer your question, it isn't a bug. I don't really know why you would need the edge to be visible in edit mode when using the mirror modifier though. If you do really need the edge to be visible for some reason, you can always click the little 3 vertex button at the top of the modifier, and that will draw all of the edges/vertices/faces like the rest of the mesh, as well as allow you to select them.